Collusion in Atomic Splittable Routing Games
We investigate how collusion affects the social cost in atomic splittable routing games. Suppose that players form coalitions and each coalition behaves as if it were a single player controlling all the flows of its participants. It may be tempting to conjecture that the social cost would be lower after collusion, since there would be more coordination among the players. We construct examples to show that this conjecture is not true. These examples motivates the question: under what conditions would the social cost of the post-collusion equilibrium be bounded by the social cost of the pre-collusion equilibrium?
We show that if (i) the network is “well-designed” (satisfying a natural condition), and (ii) the delay functions are affine, then collusion is always beneficial for the social cost in the Nash equilibria. On the other hand, if either of the above conditions is unsatisfied, collusion can worsen the social cost. Our main technique is a novel flow-augmenting algorithm to build Nash equilibria.
KeywordsNash Equilibrium Social Cost Full Version Delay Function Congestion Game
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- 2.Andelman, N., Feldman, M., Mansour, Y.: Strong price of anarchy. In: SODA, pp. 189–198 (2007)Google Scholar
- 3.Aumann, R.: Acceptable points in geneeral cooperative n-person games. Contributions to the Theory of Games 4 (1959)Google Scholar
- 6.Fotakis, D., Kontogiannis, S., Spirakis, P.: Atomic congestion games among coalitions. ACM Transactions on Algorithms 4(4) (2008)Google Scholar
- 8.Hayrapetyan, A., Tardos, E., Wexler, T.: The effect of collusion in congestion games. In: STOC, pp. 89–98 (2006)Google Scholar
- 9.Huang, C.-C.: The price of collusion in series-parallel networks, Technical Report 238, Humboldt-Universität zu Berlin, Institut für Informatik (2011)Google Scholar
- 12.Roughgarden, T.: Selfish routing with atomic players. In: SODA, pp. 1184–1185 (2005)Google Scholar
- 13.Roughgarden, T., Schoppmann, F.: Local smoothness and the price of anarchy in atomic splittable congestion game. In: SODA, pp. 255–267 (2011)Google Scholar
- 15.Wardrop, J.G.: Some theoretical aspects of road traffic research. In: Proc. Institute of Civil Engineers, Pt. II, vol. 1, pp. 325–378 (1952)Google Scholar